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C₂×#59562 #7666292

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

7616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,17)(16,18)(20,23)(21,22);(4,8)(5,9)(11,13,15,18)(12,14,17,16)(19,20,24,23)(21,26,22,25);(11,13)(12,16)(14,17)(15,18)(19,21,24,22)(20,25,23,26);(3,5,7,9)(4,6,8,10)(11,13)(12,16)(14,17)(15,18)(19,22,24,21)(20,26,23,25);(3,6)(4,9)(5,8)(7,10)(11,14,15,16)(12,13,17,18)(19,23,24,20)(21,26,22,25)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573488);